It really depends on the situation, but I usually don't like chain pulling as a DPS and I don't do it as a WAR (cause I want TP too). As a BLM I don't mind much. Even transposing will restore all MP pretty quickly (if the tank runs the mob out of blizzard range before I cast, for instance).
As a MNK there's no advantage to chain pulling unless it's a very short distance. If I'm running for more than 5 seconds I almost certainly can't hit the mob, drop greased lightning, lose out on extra TP regeneration, and then have to finish off the mob the tank was carrying without my buffs before starting on the new group. It's a loss of efficiency instead of a gain. It does work in some places though, like Stone Vigil HM. Most of the groups are close enough that, as long as I know what the tank is doing I can shoulder tackle over to the new group and not drop buffs. Still can't do this repeatedly though because of TP.